Question: Simplify the following expression: $\dfrac{2k^3}{5k^2}$ You can assume $k \neq 0$.
Solution: $ \dfrac{2k^3}{5k^2} = \dfrac{2}{5} \cdot \dfrac{k^3}{k^2} $ To simplify $\frac{2}{5}$ , find the greatest common factor (GCD) of $2$ and $5$ $2 = 2$ $5 = 5$ $ \mbox{GCD}(2, 5) = = 1 $ $ \dfrac{2}{5} \cdot \dfrac{k^3}{k^2} = \dfrac{1 \cdot 2}{1 \cdot 5} \cdot \dfrac{k^3}{k^2} $ $\phantom{ \dfrac{2}{5} \cdot \dfrac{3}{2}} = \dfrac{2}{5} \cdot \dfrac{k^3}{k^2} $ $ \dfrac{k^3}{k^2} = \dfrac{k \cdot k \cdot k}{k \cdot k} = k $ $ \dfrac{2}{5} \cdot k = \dfrac{2k}{5} $